Mirrors
The alarm beeps and you are rudely awakened from your pleasant dreams and suddenly you're thrown into the real world. You stumble out of bed and get dressed. As you are brushing your teeth and hopefully washing your face, you look up at the mirror and say 'I look wonderful today' to your reflection. What is this object you are looking in to? It's called a mirror. Most of us take this sheet of glass for granted, but as you'll soon discover, it's a complex object that involves equations to see what you see each and every mourning. History of the Mirror (History of Optics) Mirrors have existed in the world since the world's begining. The Ancient Romans used silver or any metal, highly polished it, and bent it a little so that it was convexed. The idea of putting a thin sheet of glass on top of a shiny metal background was first discovered in the 16th century. Now you may be asking who came up with all of the equations and laws of reflection? Well, there were many people in history to determine these laws, and they go back all the way to 300 BC. * A man name Euclid, who lived in 300 BC, studied reflection and recorded some basic observations on the topic in his book,Optica. He noticed that light rays traveled in straight lines, and concluded that there are rays that go from the eyes of the person to the object being observed. This theory that Euclid came up with would later be known as the Law of Reflection. http://www.visual-euclid.org/euclid.gif Some time after Euclid, a man named Heron discovered that in a plane mirror, the path that a reflected ray of light takes is shorter than any other reflected path that exists between the source and the obsever. Law of Reflection Euclid came up with the law of reflection which states that the angle of incidence (the angle from the observer to the mirror) must be equal to the angle of reflection (the angle from the mirror to the reflected object. Both of these angles are measured in respect to the normal line, which is perpendicular to the surface of the mirror. http://wps.prenhall.com/wps/media/objects/785/804514/ch26_SWA/images/1a.gif http://wps.prenhall.com/wps/media/objects/785/804514/ch26_SWA/images/1a.gif http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l1c1.gif http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l1c1.gif A graphic that illustates what occurs during the law of reflection.(Taken from physicsclassroom.com) http://www.physicsclassroom.com/mmedia/optics/lr.gif Plane Mirrors How Objects are Seen with a Mirror Plane mirrors are mirrors that are flat. These mirrors show and obey the law of reflection. When an object is placed infront of a mirror, it emits light rays on all different angles. http://www.gunn.palo-alto.ca.us/~cbakken/p1A/optics/obookshelf/image141.gif http://www.gunn.palo-alto.ca.us/~cbakken/p1A/optics/obookshelf/image141.gif The light rays hit the surface of the mirror, and they "bounce off" or reflect. The Law of reflection states the the angle of incidence (the angle of the light coming from the object hitting the mirror) is equal to the angle of reflection (the ray which bounces off of the mirror). http://www.gunn.palo-alto.ca.us/~cbakken/p1A/optics/obookshelf/image143.gif http://www.gunn.palo-alto.ca.us/~cbakken/p1A/optics/obookshelf/image143.gif As noted above, the angle of reflection equals the angle of incidence, and they are both in the same plane. To understand how the image is seen in a plane mirror, you must imagine that these angles of reflection are reflected on the other side of the mirror. These angles are still the same angles as the angle of reflection, but instead of being equal with respect to the normal line, they are equal with respect to the mirror. The point of intersection of all of the lines created by the angle of reflection is the virtual image. It is called the virtual image because the object isn't actually placed in the mirror, but the reflection of the light makes it seem as if it is. http://www.gunn.palo-alto.ca.us/~cbakken/p1A/optics/obookshelf/image145.gif http://www.gunn.palo-alto.ca.us/~cbakken/p1A/optics/obookshelf/image145.gif A graphic that illustrates how an object is seen in a mirror (Taken from www.physicsclassroom.com) http://www.physicsclassroom.com/mmedia/optics/ifpm.gif http://www.physicsclassroom.com/mmedia/optics/ifpm.gif My My My, Don't I look Fabulous This Morning(Observations in a Plane Mirror) When you wake up in the morning and give yourself a good look in the mirror, you'll notice that the image in the mirror isn't the same size as you are in real life. To see all of your body in a full length mirror, the mirror only needs to be one half of your actual height in order to see your entire body, from head to toe. http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l2d1.gif http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l2d1.gif In the graphic above, you can see that the distance from points xy, where the angles of incidence from the feet and the head meet the mirror is half as long as the image reflected from head to toe. Notice when you stand closer to the mirror, you seem a lot larger, but as you walk backwards, your image in the mirror gets smaller and smaller. http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l2d2.gif http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l2d2.gif Concaved Mirrors Definition of Concaved Mirror Concaved Mirrors are mirrors that cave inwards, towards their own centers. http://www.batesville.k12.in.us/physics/phynet/Optics/Curved%20Mirrors/Images/Concave.GIF http://www.batesville.k12.in.us/physics/phynet/Optics/Curved%20Mirrors/Mirror_Types.html There are many components to concaved mirrors. They follow the law of reflection, but because they are curved, special things happen.Imagine that a curved mirror is a slice of a sphere. Something called the principal axis, which goes through the center of the sphere, hitting the mirror in it's center. The point which would lie on the center of the sphere, is called the center of curviture and is usually denoted with the letter C''. The distance from C to the mirrors center (vertex) is 1 radii. This distance is also called the radius of curviture. The vertex is the point in which the principal axis hits the mirror, and is the center of the mirror. Halfway between ''C and the vertex is the focal point, denoted by the letter f''. C=2f Behavior of Rays There are different types of rays and how they reflect off a mirror, they all follow the law of reflection: *When a ray that is parallel to the principal axis hits the concaved mirror, it will reflect through the focal point. *Incident rays which aren't parallel to the prinicpal axis that reflect through the focal point have a reflection which is perpendicular to the principal axis. *Incident rays that hit the mirror at the principal axis, use the axis as it's normal line, and normally reflect. *A ray that goes through the point C, is reflected back through point C. http://www.batesville.k12.in.us/physics/phynet/Optics/Curved%20Mirrors/Images/Con_Rays.gif http://www.batesville.k12.in.us/physics/phynet/Optics/Curved%20Mirrors/Images/Con_Rays.gif '''The normal line is created from the point C to the point in which the angle of incidence hits the mirror. It is then reflected as described in the law of reflection.' The point in which all of these reflected rays intesect is the location of the image. http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/optics/rdcma.gif http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/optics/rdcma.gif Real Images The location of the image depends on the placement of the original object.The following are all real images(a real image is formed whenever reflected light passes through the image location): *If the object is placed at point C'', then the image is also at point C. **The object will appear inverted, and have the same dimensions as the object. *If the object is placed between ''C and f'', the image will be located behind(away from the mirror) ''C **The object is inverted and magnified, or larger than the object. *If the object is placed beyond C'', then it's image is located infront of ''C (towards the mirror) **The image is inverted, or upside down, and appears to be smaller. Virtual Images A virtual image is created if the object is located less than one focal length (f'') from the mirror. This follows the law of reflection as well, but a virtual image is created, much like the plane mirrors. This virtual image is magnified, and is upright. http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l3d7.gif There is no image if the object is located at the focal point. Spherical Aberration Spherical abberation occurs when light rays hit the mirror near it's edge, and the rays don't focus on the same point that all of the reflected rays from the center of the mirror focus's on.This can leave the image to be fuzzy and blurry. http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l3g1.gif http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l3g.html Above, we can see that the two rays that hit the top and bottom edge of the mirror obey the law of reflection, but they don't meet the focal point like all of the other rays. Convex Mirrors http://www.batesville.k12.in.us/physics/phynet/Optics/Curved%20Mirrors/Images/Convex.GIF http://www.batesville.k12.in.us/physics/phynet/Optics/Curved%20Mirrors/Mirror_Types.html All of the points that are used to create ray diagrams for convex mirrors are the same as for concaved mirrors, except that they are ''behind the mirror. Definition of Concaved Mirror When the object placed infront of the mirror emits light rays, they reflect off of the convexed mirror according to the law of reflection. Though the reflected rays will never intersect in the object's plane, they do intesect behind the mirror, forming a virtual image. The point of intersection for all of reflected rays behind the mirror is the image location. Behavior of Rays The rays have different patterns of reflection depending on the position of the incident ray. The behavior is explain below: *Any incident ray parallel to the principal axis will reflect in a way that its extension will pass through the focal point. *Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis. *A ray that hits the mirror at the principal axis is reflected at the same angle. Mirror Equations The mirror equations are used to calculate the sizes and distances of the images that are formed by the curved mirrors and the objects. http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l3f1.gif http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l3f2.gif Where o'' is the original object, and ''i is the image. d'' is the distance from the mirror, and ''h is the height of the object or image. M'' is the magnification, and ''f is the focal point. When the image, object, or focal is real, then the distances are positive. When the image,object, or focal is virtual, the distances are negative. http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l4a3.gif http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l4a3.gif Sample Questions 1.An Object whose height is 0.15 meter is placed .60 meter from a concave mirror whose focal length is 0.20 meter. (a)Where is the center of the curviture of the mirror? (b)Where is the image located? ©What is the height of the image? 2.A student stands 2.0 meters in front of a vertical plane mirror. As the student walks toward the mirror, the image (1)decreases in size and remains virtual (2)decreases in size and remains real (3)remains the same size and remains virtual (4remains the same size and remains real 3.An incident light ray travels parallel to the principal axis of a concave spherical mirror. After reflecting from the mirror, the light ray will travel (1)through the mirror’s principal focus (2)through the mirror’s center of curvature (3)parallel to the mirror’s principal axis (4)normal to the mirror’s principal axis 4.The focal length of a concave spherical mirror is 0.060 meter. What is the radius of curvature of the mirror? (1)0.060 m (2)0.12 m (3)8.3 m (4)17 m 5.Images formed by diverging (convex) mirrors are always (1)real and inverted (2)real and erect (3)virtual and inverted (4)virtual and erect 6.A spherical mirror that forms only virtual images has a radius of curvature of 0.50 meter. The focal length of this mirror is 1.-0.25 m 2.+0.25 m 3.-0.50 m 4.+0.50 m 7.A spherical concave mirror is used in the back of a car headlight. Where must the bulb of the headlight be located to produce a parallel beam of reflected light? 1.between the principal focus and the mirror 2.beyond the center of curvature of the mirror 3.at the principal focus of the mirror 4.at the center of curvature of the mirror 8. A light ray is incident upon a plane mirror. As the angle of incidence increases, the angle between the incident ray and the mirror's surface: a.Decreases b.increases c.remains the same 9. An object is placed infront of a convex mirror. The image of the object will be a.nonexistant b.real and smaller c.wirtual and smaller d.virtual and larger 10.If the distance between and onject and a concave mirror is more than twice the focal length of the mirror, the image formed will be a.real and behind the mirror b.real and in front of the mirror c.virtual and behind the mirror d.virtual and in front of the mirror 11.An object is located .12 meter infront of a concave mirror of .16-meter radius. What is the distance between the image and the mirror? a.0.07m b.0.20m c.0.24m d.0.40m Solutions 1.a. 0.40m,1.b. .30m,1.c.-0.075m,2.'3,'3.'1,'4.'2,'5.,'6.'1,'7.'3,'8.'1,'9.'3,'10.'2,'11.'3] Resources and References Since I used most of the resource sites to help me learn the topic, they are both references for this page, but if you are looking for additional help with mirrors, these sites will also help explain things as well. 1.History of Mirrorshttp://www.mirrorresilvering.com/a_brief_history_of_mirrors.htm 2.History of Optics Timelinehttp://web.archive.org/19990222135012/members.aol.com/WSRNet/D1/hist.htm 3.Types of mirrors (most images borrowed from this site)http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l2d.html 4.Plane Mirrorshttp://www.gunn.palo-alto.ca.us/~cbakken/p1A/optics/obookshelf/pmirror.html 5.Curved Mirrors (most images borrowed from this site) http://www.batesville.k12.in.us/physics/phynet/Optics/Curved%20Mirrors/Mirror_Types.html 6.Barrons Regents Review Book 7. All Types of Mirrors http://www.physicsclassroom.com/Class/refln/reflntoc.html 8. Mirrors and reflection http://farside.ph.utexas.edu/teaching/302l/lectures/node105.html 9. An experiment to further the understanding of how converging mirrors work http://www.rowan.edu/colleges/las/physicsandastronomy/LabManual/labs/LensesAndMirrors.pdf 10.Plane mirrors http://online.cctt.org/physicslab/content/Phy1/lessonnotes/planemirrors/planemirrors.asp 11. Reflection http://scienceworld.wolfram.com/physics/Reflection.html 12. Spereical Abberation http://en.wikipedia.org/wiki/Spherical_aberration